In Euclidean geometry, the orthogonal projection is one whose auxiliary projecting lines are perpendicular to the projection plane (or to the projection line), establishing a relationship between all the points of the projecting element with the projected ones.[1]​.

In the plane, the orthogonal projection is one whose auxiliary projecting lines are perpendicular to the projection line L.

Thus, given a segment AB, it will be enough to project the "extreme" points of the segment – ​​using auxiliary projecting lines perpendicular to L – to determine the projection onto the line L.

An application of orthogonal projections is the theorems of metric relations in the triangle by which the dimension of the sides of a triangle can be calculated.

The concept of orthogonal projection is generalized to Euclidean spaces of arbitrary dimension, even infinite dimension. This generalization plays an important role in many branches of mathematics and physics.